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Fibonacci/Golden ratio = 1.618 Kilometres in 1 mile = 1.609
Conversion is off by less than 1%, not bad at all
Yeah, it's nice and mysterious the first moment you hear about this but all the romance is gone once you think about how it works.
By far the most complicated part is the fact that the ratio of successive terms in the Fibonacci sequence approaches a specific number (which happens to be the golden ratio, which happens to be close to the ratio of km/mi).